 # 3. Genesis of the Cabibbo-Kobayashi-Maskawa Matrix

by Dr. Bruce McLaughlin

This article presents evidence suggesting that the nine elements of the CKM Matrix, which are integral to the Standard Model of Particle Physics, flow from the first twelve characters of the first verse of Genesis.

Introduction

A Judeo-Christian tradition is that God arranged the 304,805 character string of concatenated words in the Torah to reveal not only a spiritual message but also to encrypt fundamental information about the beginning of the universe and its development over time including the entirety of physics, chemistry, biology and human history… a message within a message.

In Genesis of the Reciprocal Fine Structure Constant by B. McLaughlin, several critical dimensionless numbers of physics/mathematics are predicted from the first 12 characters of the first verse of Genesis.  Is it possible that this same string of 12 characters provides information about fundamental parameters of particle physics?

Background

The magnitudes of the nine CKM matrix elements are given by:

0.97427 (+0.00015             0.22534 (+0.00065             0.00351 (+0.00015

-0.00015)                            -0.00065)                            -0.00014)

0.22520 (+0.00065             0.97344 (+0.00016             0.0412 (+0.0011

-0.00065)                            -0.00016)                          -0.0005)

0.00867 (+0.00029             0.0404 (+0.0011                 0.999146 (+0.000021

-0.00031)                          -0.0005)                                  -0.000046)

These magnitudes indicate the probability of transition from one quark to another.

Analysis

The first three, second three and third three characters from the first verse of Genesis can be expressed as

 020 212 020 Ayz = 000 Byz = 001 Cyz = 000 110 200 110

reading left to right as the Text is read from right to left. Each of the Hebrew characters is represented by a base-3 triplet (column vector) according to a rule that starts with Aleph as (000) and ends with Tsadey Final as (222).  If these three matrices are arranged in a Rubik Cube configuration, fifteen 3 by 3 matrices are produced by taking slices through the cube.  Each slice produces 8 matrices by rotation about various axes; dihedral group of order eight (D4).  In this trial, only one matrix will be selected for each slice.  We still find ourselves short by one 3 by 3 matrix in order to construct a single matrix of dimension 12.  We will add a single 3 by 3 matrix representing the fourth three characters from the first verse of Genesis.

 010 XXX = 001 021

A 12 by 12 matrix M can be constructed from these four matrices as illustrated in Genesis of the Reciprocal Fine Structure Constant by B. McLaughlin.  This matrix M is:

 0 2 0 2 1 2 0 2 0 1 2 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 2 0 0 1 1 0 0 2 0 0 2 0 2 1 2 0 2 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 2 1 1 1 0 0 2 0 0 0 0 1 1 0 1 0 0 2 1 2 0 0 1 2 0 0 0 0 1 0 2 0 0 0 0 1 1 0 0 0 0 1 1 0 0 2 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 2 0 0 0 0 0 0 0 0 2 1

Now define X = MM*, Y = X2 and Z = X3 where M* is the transpose of MX, Y and Z are each 12 by 12 matrices and each will have a characteristic equation with twelve coefficients.  Let the coefficients for X, Y and Z be denoted by J1…J12, JJ1…JJ12 and JJJ1…JJJ12 respectively.  Next form the following 6 by 6 matrix, designated as j1, from the 36 coefficients of the three characteristic equations?

JJJ1    J1         J2       JJJ12   JJJ11     J12

JJJ2    J6         J3       JJ7        JJ8          JJ9

j1  =   JJJ3    JJ1       J7       JJ6        J10         JJ10

JJJ4    JJ2       J4        J8         J5            JJ11

JJJ5    JJ3       JJ4      JJ5       J9           JJ12

JJJ6    JJJ7    JJJ8    JJJ9     JJJ10    J11

This particular matrix is just one of 36! matrices that can be formed from the 36 coefficients.  Now form the symmetric matrix k1 = j1 j1* and evaluate cosk1 = Cos[k1], sink1 = Sin[k1], p1 = Cos2[k1], q1 = Sin2[k1] and r1 = Sin[k1]Cos[k1].  These five expressions use the power series for Sin and Cos with ordinary powers replaced by matrix powers.  The result is five, 6 by 6 symmetric matrices with the absolute value of each element between zero and one. So, how might CKM magnitudes be encoded?  One way is to combine no more than two selected matrix elements from p1, q1 and r1 using basic arithmetic – addition, subtraction, multiplication and division – while viewing the elements themselves as floating point numbers; in other words, the decimal point can be shifted to the right or left.  Here is a sample finding:

CKM11 = 10 r1[[2,3]] + 10-1 r1[[2,2]] =            0.974345

CKM22 = 10 r1[[2,3]] – 10 p1[[1,3]] =              0.973407

CKM33 = 10 r1[[2,3]] -10 r1[[1,4]] =                0.999177

CKM12 = - r1 [[2,2]] + 10 q1[[4,5]] =                0.225462

CKM21 = - r1[[2,2]] + 10-1 r1[[2,2]] =               0.225031

CKM13 = r1[[3,4]] =                                                  0.0035343

CKM31 = 103 r1[[3,5]] + 10 r1[[1,4]] =            0.0086507

CKM23 = - 10-1 r1[[5,5]] + 10-2 r1[[2,2]] =     0.0413213

CKM32 = - 10-1 r1[[5,5]] – r1[[3,4]] =               0.0402874

Conclusions

The predicted CKM matrix from this sample is:

0.974345          0.225462          0.0035343

0.225031          0.973407          0.0413213

0.0086507        0.0402874        0.999177

which is consistent with the confidence limits of the actual CKM Matrix of Magnitudes.  Also, only seven elements of r1, one element of p1 and one element of q1 were used to define these nine elements.  This suggests a functional relationship exists between the various elements of the CKM matrix.

These findings could represent a completely serendipitous coincidence.  Or they might suggest a causal connection between God and the Standard Model of Particle Physics.  At the very least, these findings demonstrate how the CKM Matrix of Magnitudes can be generated from four 3 by 3 matrices with elements 0, 1 and 2 where two of the matrices are identical.